But his efforts, unfortunately, were not enough to take his side to a win as Ruben Loftus-Cheek missed his kick from the spot in the penalty shootouts, giving Arsenal the victory.
The Gunners will be looking to at least break back into the top four next season after they ended up in sixth place and without a trophy last term.
Teenage forward Hudson-Odoi then breezed past Bellerin on three occasions to create chances for Morata before the interval.
Cesc Fabregas' shot, after a fine run from Hudson-Odoi, was turned behind by Cech and from the resulting corner the unmarked Rudiger rose highest to power home a header.
Chelsea continued to create chances, with Morata's header following Hudson-Odoi's cross deflected for a corner.
"Hudson-Odoi is a very young player", he said.
Chelsea boss Maurizio Sarri replaced Fabregas with Danny Drinkwater and sent on Andreas Christensen for David Luiz during the interval.
Sarri made further changes in the 63rd minute when Davide Zappacosta, Emerson, Victor Moses and Tammy Abraham replaced the Spanish quartet of Cesar Azpilicueta, Marcos Alonso, Pedro and Morata.
The late goal meant a second successive penalty shoot-out for Chelsea, who recently won against Inter Milan but were beaten 6-5 this time.
- Trump thanks Kim for handing over remains of war dead
- How Google reversed its course on opposition to censorship in China
- Dixons Carphone hikes to 10-million clients’ personal data accessed by hackers
- Deal to fight Wilder in December ‘almost done’, says Tyson Fury
- Judge stops 3-D guns hours before U.S. release
- Wildfires scorch homes, land - and California's firefighting budget
- Apple becomes world's 1st trillion-dollar company
- Pope Francis accepts Adelaide Archbishop Philip Wilson's resignation
- North Korea Returns Remains of Korean War Dead to US
- Kim Kardashian enjoys being labelled ‘anorexic’ by sisters